Elastic fluid turbine



Oct. 14, 1941.

5. WAY

v ELASTIC FLUID TURBINE 2 Sheets-Sheet 1 I Filed May 16, 1940 FI I.

IINVENTOR 5 TEWR RT We )4 WITNESSES.

ATTORN EY Patented Oct. 14, 1941 I ELASTIC FLUID TURBINE Stewart Way,Forest Hills, Pa., assignor to West inghouse Electric & ManufacturingCompany, East Pittsburgh, Pa., a corporation of Pennsylvania ApplicationMay 16, 1940, Serial No. 335,465

13 Claims. (01. 253-39 My invention relates to elastic-fluid turbinesand it has for an object to provide-vane elements suitable for elasticfluids moving at superac oustic velocities.

A more particular object of the invention is.

' pression shocks. I While the invention may be employed either fornozzle vanes or for rotor blades or buckets, it is particularlyapplicable to the first row of rotor blades of the impulse type'andwherein,

usually steam moving at super-acoustic velocities is encountered. Aconventional type of turbine is a two-row Curtis impulse stage followedby reaction or Rateau stages, and a substantial fraction of theavailable energy of the steam is converted into mechanical energy by theCurtis stage; however, as the eficiency of a Curtis stage is relativelylower than a reaction stage, the overall eificiency is reduced onaccount thereof. With the incorporation of the new type of blading inthe first row of rotor blades, or in subsequent rows if super-acousticvelocities should occur therein, the efiiciency is improved on accountof the improved performance of the new type of blading in dealing withelasticfluids moving at super-acoustic velocities. With the conventionaldesign, super-acoustic velocities occur only in the first row of blades,so that it issuificient to restrict the incorporation of the new type ofblading tothatrow. a H

One reason for the lower efficiency of the initial impulse bladingis-bound up with itsgoperation at super-acoustic entering steamvelocities. In super-acoustic gas flow, compression shocks occur 'under.certain conditions that result in an increase in entropy, therebyrendering unavailable a certain portion of the energyinitially avail-'able in the steam for doing work. Heretofore,

' impulse blading has been designed withpractically no attention beinggiven to the possible ccurrence of compression shocks in the passages.

Accordingly, a more particular object of my invention is' to improve theefficiency. of the, initial row or rows of impulse blades for handlingelastic fluid moving at super-acoustic velocities by having the convexfaces thereofiiormed with corner or corners and theconcave facescooperating with the convex faces to-define flow passages. providthatthe latter will be capable of inducing the adjacent stream to turnwithout other mechanical constraint, and without the occurrence ofcompression'ghocks. I

A further object of the invention is to provide blade passages with theconvex faces having corners to induce turning of the stream in eachpassage and wherein the passage sections increase in the direction offlow and the corners ar rounded.

A further object of the invention is to provide a row of turbine bladeshaving concave and po-' lygonal convex faces defining blade passages forthe reception 'of super-acoustic velocity elastic fluid and wherein thefluid is induced to turn by I the corners, each convex face having threecorners to afford a suitably large total turning angle and to provideblades of adequate mechanical strength. V

- The fact that a corner in an expansion environment will induce acompressible medium moving at super-acoustic velocity to turn withoutother mechanical constraint was observed and analyzed by 'Prandtl-Meyer(see analysis of Prandtl-Meyer found in Aerodynamic Theory by Duran,volume III, division H, chapter 4, section 4, pages 243-246, and SteamTurbines,'Stodola- Lowenstein (1927), volume II, pages 983-5Q-and may beregarded as the Prandtl-Meyer streamline efiectu The present inventionhas for an object to utilize the means responsible for this efiect'inconnection with impulse turbine vane '"velements to improve theefliciency thereof.

Fig. 5 is a diagrammatic ing; and,

' "These and other objects are effected by. my invention as will beapparent from the following description and claims taken in connectionwith the-accompanying drawings, forming apart of this application, inwhich:

Figs. 1, 2 and Bare diagrams'illustrative of the Prandtl-Meyerstreamline;

Fig. 4-is a diagram showing the theory of operation of the improvedblade passage;

view showing certain geometric aspects;

Fig. 6 is a sectional view of the improved bladvelocity turning efiect,-the convex faces .of the vanes or blades having oneor more corners anding such pressure conditionsabout each corner. the concave facescooperating with the convex is parallel to the rigid boundary A0, thecorner being at 0. When the fluid reaches the corner,

instead of continuing therebeyond in a straight path, it curvestherearound and resumes movement in a straight path after angulardeflection dependent upon expansion from the region I of higher pressureto the region II of lower pressure, the excess of actual velocity of thestream over the acoustic velocity, the ratio of the actual velocity tothe acoustic velocity being known as the Mach number. In Fig. 1, thestream curves from the radius vector GM to the radius vector ON; and theextent of turning depends upon the Mach number of the approaching fluid,the larger the Mach number, the larger theangle of turn and vice versa.In the zone of turning, the flow is along streamlines which have suchrelation that the component of velocity (v) perpendicular to the radiusvector is always equal to the speed of sound at the conditions ofpressure and density existing at the vector, this being set forth inAerodynamic Theory, supra, page 244, as follows:

Thus, in two-dimensional flow around a corner, the component of velocityperpendicular to the radius vector must always equal the speed of soundat the local conditions of pressure and density.

In other words, within the angular limits inand "k is the specific heatratio (1.30 for superheated steam). Where n is the value of r when 0:0,any curve C (Fig. 3) consisting of combinations of arcs ab of C (where aand!) are any two points on C) or of arcs ab of C with straight linesegments, subject to the condition that the 'end points of adjacent arcson C shall be one and the same point on curve C; such. a curve C isherein referred to as a Prandtl-Meyer streamline. Curve C is astreamline for the irrotationai flow of a frictionless gas (in twodimensions) around a corner, without compression shocks. I

Since it is desirable to have the passage as wide as possible, thestreamline which forms the basis of the convex face should be onecorresponding to r=0; and, for any given angle 0, such a streamlinetherefore reduces to a point. The flow field typified by stream lines Cis such that along any ray, for 0=constant, the velocity is constant indirection and magnitude, and

p the state quantities of the gas are also constant.

dicated, such limits being dependent upon the Mach number of theapproaching fluid and the pressure drop from the region I to region II,an infinite number of radius vectors may be conceived of as existingbetween the limits; and along each radius vector the conditions ofstate, such as pressure, temperature and specific volume, are constant.Accordingly, along the radius vector OM, these conditions of state areconstant and coincide with .those of the parallel approaching stream,and the same is true with.

respect to the final vector 0N and the stream flowing paralleltherebeyond.

As shown, the stream leaves in a parallel path which may be regarded asparallel to a straight gaseous envelope OB. If OB is replaced by structure so that the corner becomes .AOB, then there would be definitestructural surfaces parallel to the parallel flow streamlines. Such aconforming corner is used with the turbine blades or vanes ashereinafter pointed out.

The definition of a Prandtl-Meyer streamline will be understood from aconsideration of the diagrams of Figs. 2 and 3.

Referring to Figs. 2- and 3, in the polar coordinate system, 1' is afunction of 0 and defines the curve C as follows:

where Therefore, each flow fleld terminating along a line, for0=constant, can be joined directly to a uniform fleld of flow of theproper pressure, temperature and velocity. A straight line OB (Fig. 1),therefore, can be used as a part of the boundary of the convex face ofthe blade passage.

As a Prandtl-Meyer streamline may be entirely curved or comprisestraight and curved portions, to take advantage of this in connectionwith turbine blades or vanes, I provide the convex faces of the latterwith corner or corners extending longitudinally thereof to induceturning with preservation of the Prandtl-Meyer streamline flow along theface. Preferably, each convex face is polygonal or comprises flatportions joined by corner portions. Adjacent to the convex face, theflow is made up of straight portions parallel to the flat portionsjoined by curved portions, the curved portions increasing and thestraight portions decreasing in linear extent out? -wardly radially fromthe convex face until the havior of a super-acoustic gas velocity streamin such a passage may be observed by the Schlieren photographic method,the corner flow phenomenon being manifested either on a ground glassplate or on a photograph by a mutiplicity of lines (Mach lines)radiating from the corners.- Assuming the fluid to enter the right-handend of the passage with a Mach number of MI. in excess of unity, then itundergoes compression from the initial Mach line Li, L: and Le to thethroat sections 0:, O4 .and 0a and expansions from the latter to thefinal Mach lines L2, L4 and La, the fluid reaching acoustic velocity atthe throat sections and moving at super-acoustic velocities at thelarger sections 01, 0:, O5 and 01. The fanlike radiating lines at eachcorner are Mach lines or linesof constant state. The Mach number hasmaximum values at the outer marginal lines L1 to Le, inclusive, andunity value at 02, and then increases, for example, to M2, greater thanunity, at the final line L2 of the comer 02. As indicated, the expansionfrom the final corner or throat section Os is for a final angle ofturning and for a Mach number, the same as at the entrance.

If a passage, such as shown in Fig. 4, having elastic medium passingtherethrough at superacoustic velocity, is subjected to Schlierenphotographic examination and the fanlike arrangement of radiating linesat each corner does not appear, then this signifies undesired shock orcompression losses, that is, the passage would not be functioning togradually reduce the Mach number at the compression side from a maximumto unity and then gradually increase the Mach number from unity to amaximumat the expansion side.

While the theory of a compressible non-viscous medium is fundamental tothe present invention, nevertheless, all real media are viscous; and,for this reason,'certain departures from the theoretical design arenecessary. Accordingly, the corners are rounded to accommodate friction,the turning angle to the first throat is restricted to avoid shock atthe entrance, and,

I because of friction, the sectional areas gradually increase from theinlet to the exit end of the passage. Having determined a theoreticalpassage for a non-viscous medium, then with such a passage as a basis,the requisite corner rounding and relationship of passage areas issecured in order to obtain flow without compression shock, the operationof an effective passage being indicated by Schlieren photographicexamination. Having determined in this way what modifications should bemade to the theoretical passage, then the practical application of theinvention merely involves the utilization of such determinations.

In Fig. 6, there is shown a multiplicity of turbine blades l suitablefor dealing with steam moving at super-acoustic velocities. The bladeshave convex faces ll'cooperating with concave faces 12 to define bladepassage 13. Each convex face ll, instead of being curved, as heretofore,is polygonal, or made up of a multiplicity of flat portions Hi, l5, l6,and ill joined by corner portions i8, i9, and 2B. The passages definedby the concave and convex faces provide for such expansion or pressuredrop about each of 'the corner portions i8, i9, and 20 that the latterinduce, without other mechanical constraint, the elastic fluid to bedeflected or turned. If the concave faces conformed exactly, they wouldhave Prandtl-Meyer streamline curvature; however, often a circular arcis so close thereto that it may be used Just about as effectively and ispreferable for manufacturing reasons.

As shown, the corners l8, l9, and 2B are rounded to the extent requiredto widen the passage'to accommodate the larger volume of fluid onaccount'of friction and to reduce shock losses, the sections 01 to 01,inclusive, being made progressively larger. Also, to avoid shocks at theentrance, the turning angledown to the first throat section 02 is madesomewhat smaller than that theoretically corresponding to the Machnumber.

The importance of avoiding compression shocks can be seen from thefollowing example.

perheated steam flowing with a velocity 1.523 times the acousticvelocity, as would result from expansion fr0m 1200 lb./'sq. in. abs;pressure to 300 lb./sq. in. If a normal compression shock occurs in sucha stream there will be an increase fore not convert the energy of thesteam as ef-' ficiently' into mechanical work as would be the case ifthe steam were flowing at the pressures and densities for which thepassages are designed. The compression shocks therefore not only giverise to an essential loss of available energy right at the shock, butalso render the flow such that energy conversion cannot be soefiiciently carried out in the impulse blading.

For a given blade width and angle of turning, the design of the elasticfluid passage to provide for Prandtl-Meyer streamlines involvesconsideration of the Mach number, M, which is the ratio ofthe actual tothe acoustic velocity, the Mach angle a, which is the calculated angle0, and the turning angle 11,

which is equal to cz+090. The angles and relations are identifiable fromFig. 5. Assuming elastic fluid to enter at the right with a Mach numberof Ml, the Mach angle on is readily ascertained from the relation YIllavingfound the Mach angle :11, the derived angle 01 is found from therelation and, knowing 01, the turning angle v1 is readily Suppose wehave a super-acoustic stream of sufound from the equation:

With three corners, as in Fig. 5', in which'the concave face has beenreplaced by a circular arc, a total turning angle of 0, a final turningangle of vc=v1, then the remaining turning angles may be made equalandfound from the relation Referring to any particular triangular flowfield, such as that between L1 and 02, a unique relation exists. betweenthe Mach number at L1 and the turning angle from L1 to 02. Also arelation exists between this Mach number and the ratio of the areas atO1 and O2. Assume that, at 02, the gas has been compressed until thevelocity is acoustic and the Mach number is 1'. The maximum and minimumsections are located relatively to one another as determined by therelation between r and 0 for a stream line,

angle that can be secured in a passage with If we had such a compressionshock in one throat O2 is theoretically dependent on the Mach number M1of the entering Jet and the constant-k, as shown by-the equations above.With two throat sections any turning angle up to 180 can theoreticallybe obtained, since the Mach number at need not be any pre-assignedvalue, but is determined by halt the turning angle from O2 to 04. Fromconsiderations of minimizing the effects 01 wall friction, it is oftendesirable to use more than two throat sections, though only two aretheoretically required, for, by using three throats instead of two, oneis sometimes led to a passage with a greaterratio of width to length.-Also, in applying the theoretical passage form in an actual turbine,considerations of blade strength and thinness of leading edge may tendto favor three throats over two.

The fluid at the initial larger area 01 and at super-acoustic velocityundergoes compression with decrease in velocity until the acousticvelocityis reached at the initial corner or throat section 02". From thelatter section to the second larger section 03, the stream undergoesexpansion with increase in velocity to a superacoustic value, followedby compression and reduction in velocity to the acoustic value at thesecond corner or throat section 04. and so on for the succeeding largerand smaller sections.

By the use of a multiplicity of. corners, the desiredtotal turning angleis attained with the preservation of Prandtl-Meyer streamline flow inthe passages. The calculated passage is shown in dot-and-dash lines inFig. 6, superimposed on the actual passage.

The threat dimension 04. for the calculated or theoretical passage isthe sameas Oz and the entire passage is symmetrical with respect to amedian blade rotationplane. The actual passage involves modification ofthe calculated passage to accommodate friction and avoid consequentcompression shocks, the modification involving rounding of the corners,restriction of the initial tuming' angle (vi), the intermediate turningangles 2 to 215) being increased to compensate and progressively openingup the passage. The throat sections 02 and 04 oi the actual passage areadvanced upstream from their theoretical locations. The progressiveopening up of the passage results in a larger projected opening on theexit plane than on the entrance plane of the wheel, and compensation toequalize the pitch at the inlet and the exit to make possible apractical blade construction may be accomplished by reducing the inletangle and increasing the exit angle. For example, if the total turningangle is 130, this would give inlet and exit angles of 21, but thepassage, with these angles, would have a larger pitch at the exit thanat the inlet side. Therefore, to equalize the pitch at both sides, theinlet and exit planes are oriented, without changing the passages, todecrease the inlet angle and to increase the exit angle to the same. ex-

In the example given, the inlet angle a Mach number of 1.95, a nozzleangle of 15, and

Assuming that the concave face is a circular arc, then R= -;=0.808 inch138 2 sin T and =sin" ==sin' -==30 51' M 1.95 for superheated steam,

k-l E 0.36115 The Prandtl-Meyer functions a and 0 are related by thefollowing equation:

sin a k-1 2 cos M and from which (For a Mach number of 1.95, and k=l.300the stream may be turned 27 07' in reducing the velocity just toacoustic.)

The half-chord length z1=R sin v1=0.366 inch r (initial Mach 1ine)==0.367 inch =0.112 inch g= (cos M9 m2 -a.3o17 The first throat dimensionshould be 0.367 O, (Prandti-Meyer) -OJII? From this, it will be seenthat the error introduced in this case on account of the circular arcapproximation to the Prandtl-Meyer stream line Applying the law ofcosines r; (0.803) +(0.691) 2(0.803) (0.691) cos 20 56.5

(Prandtl-Meyer) 293 and from this and from the relation L il sin oft-1L2cos A6 0z=78 6 min., and =33 57 min.

In Fig. 5, the angle ODE=-02-a2=57 57 min. Designating DE by x and 0E byu,

:1: cos 67 5'7 lnin.+y cos 20 56.5 min.=0.69l a; sin 67 57 min.=y sin 2056.5 min.

= (cos 719-103 mechanical constraint.

may be provided utilizing the corner-turning As the sections 01 and 01are equal, the sections 02,0 and O6 are equal and the sections 03 and 05are 'equal, the calculation gives the following forthe theoreticalpassage:

Position Location Opening Deg. Min. 0 188 O2 27 7 112 0a 48 04 162 O4 69112 O5 89 57 162 0a 110 53 112 O 1 138 188 The calculation is for atheoretical non-viscous elastic fluid; however, as all real elasticfluids are viscous, modifications, as hereinbefore indicated,

'must be made to the theoretical passage to accommodate friction andavoid consequent compression shocks, the modifications being made untilthe Schlieren picture presents an appearance with good distribution ofMach lines at each corner. The modification involves corner rounding andopening up between corners to obtain restriction of the initial turningangle and progressive opening up of the sections until a satisfactorypassage is reached. Such modification would involve relocation upstreamof the first and second corner sections and progressive opening of thesections. For example, the modified section positions and sectionopenings may be:

- Position Location Opening Degrees O1 0 0. 185 O1 25 0. 134 0a 48 0.166 O4 68 0. 146 O5 90 0. 182 O0 111 O. 162 O1 138 0. 218

It is to be understood that the theoretical calculation, as well as themodifications, are given by way of example only to make the inventionclearer and to indicate a procedure which may abstraction stage oftheCurtis type wherein, in addition to the improved blades ill used inthe.

If the initial Mach number is high enough and the total turning angledesired is sufficiently small, fewer corners can accomplish the tuming,but, for mechanical. reasons, with blades having concave and convexfaces providing for Prandtl-Meyer streamline flow, 'not less than threecorners can effect a total turning angle of the order suggested. On theother hand, the

number of corners should not be excessive in order to avoidlong slenderpassages which would increase wall friction.

In Fig. '6, the blades Ill providing -Prandtl- Meyer streamline, fiowpassages I3 have elastic fluid supplied thereto by suitable nozzles 2|(one being shown) of suitable expansion ratio,

In Fig. 7, there is shown a multiple-velocityfirst moving row, thenozzles 23 are also constructed and arranged so that corners 24 in duceturning of the fiuid stream in the passages, with the result thatnozzles of adequate expansion ratio to give the desiredsuper-acousticvelocitywith. a minimum of shock are provided.

be followed to arrive at practical realization from the theoreticalbasis. It may be possible to attain the ultimate structure by. othermethods or the procedure may, at some time, be simplified by beingreduced entirely to a calculation basis.

After all, the invention is for aturbine wherein -the blading convexblade faces are polygonal in order to secure Prandtl-Meyerstreamline-flow in the blade passages, the passages providing suchexpansions or pressure drops about the-corners that the latter induceturning Without any other phenomenon, that is, having Prandtl-Meyerstreamline flow in the passages, it is first of all necessary tocalculate and design the passage for a theoretical non-viscous elasticfluid and then to modify the passage suitably for a real or viscousfluid to accommodate for friction and avoid consequent shock losses. Thenumber of corners provided on the convex face must be such that therequired total angle In order that blades.

form, it will be obvious to those skilled in the art that it is not-solimited, but is susceptible of various changes and modifications withoutdeparting from the spirit thereof, and I desire, therefore, that onlysuch limitations shall be placed thereupon as are specifically set forthin the appended claims.

What I claim .is: i

1. In a turbine, a row of vane elements having inlet and outlet edgesand convex and concave faces extending therebetween and providing pas- Fsages for elastic fluid delivered thereto at superacoustic velocity,said passages having the convex faces thereof-formed by flat portions,in

cluding fiat portions extending to the inlet and outlet edges of thevane elements, and three or more corner portions joining successive fiatportions and said passages providing pressure conditions about eachcorner portion such that the latter is capable of inducing, withoutother me chanical constraint, turning of the fluid stream in its passagewithout compression shocks.

2. In a turbine, a nozzle for discharging elastic fiuid atsuper-acoustic velocity, a row of vane elements having sharp inlet andoutlet edges and convex and concave faces extending between the latterand providing passages for elastic fluid delivered thereto by thenozzle, said passages having the convex faces thereof formed by fiatportions, including fiat portions extending to the inlet and outletedges, and three or more cor'nerportions joining successive fiatportions and said passages providing pressure conditions about eachcornerportion such that the of turning may be efiected, while, at thesame time, preserving adequate mechanical strength in the blades each ofwhich must be formed with a concave and convex face. For example, with ablade width of 1.5" and the customary turning angle for a row of impulseblades, for example,

from to three corners seem necessary.

latter is capable of inducing, without other mechanical constraint,turning of the fluid stream in its passage without compression shocks.

. 3. In-a turbine, vane elements providing passages for elastic fluidmoving at superacoustic velocities and defined by concave and polygonalconvex faces the. polygonal convexfaces providrespectively, rection offiow.

ing fiat portions separated by corners and the comers being rounded, thefiat portions and the corners of each convex face cooperating with theopposed concave face to provide, respectively, maximum and minimumsections of the passage and to provide for convergence of the passagefrom the maximum sections to the minimum sections and for divergencethereof from the minimum sections to the maximum sections and the cornersections progressively increasing in area from the inlet end to theoutlet end of each passage.

4. The combination as claimed in claini 3 wherein the outermost fiatportions of the polygonal face of each blade define, with the concaveface, sharp inlet and outlet blade edges.

5. In a turbine, a row of moving impulse blades providing passages forelastic fluid moving at super-acoustic velocities and defined by concaveand polygonal convex faces, the passages pro-- viding such pressureconditions about the corners of the polygonal faces that such cornersinduce turning of the fluid in the passages without other mechanicalconstraint, the corners of the convex polygonal faces being rounded andthe turning angle to the first throat section and defined by the firstcorner with respect to the concave face being sufficiently less thanthat corresponding,

to the Mach number of the entering Jet to avoid compression shock at thepassage entrance 6. In a turbine, a row of blades for abstracting energyfrom elastic fluid delivered thereto at super-acoustic velocity; saidblades having convex and concave faces providing blade passages and eachconvex face being polygonal with the corner portions thereof rounded andjoining successive fiat portions; the corner portions of the convexpolygonal faces defining, with respect to the concave faces, throatsections and the flat portions defining, with respect to the concavefaces, maximum sections ahead of, intermediate and following the throatsections of each passage and said throat sections being progressivelylarger in the direction of flow.

'7. In a turbine, a row of blades for abstracting energy from elasticfluid delivered thereto at super-acoustic velocity: said blades havingconvex and concave faces providing blade passages and each convex facebeing polygonal with the corner portions thereof rounded and joiningsuccessive fiat portions; the corner portions of the convex polygonalfaces defining, with respect to the concave faces, throat sections andthe fiat portions defining, with respect to the concave faces, maximumsections ahead of, intermediate and following the throat sections ofeach passage and said throat and maximum sections, respectively, beingprogressively larger in the direction 8. In a turbine, a row of bladesfor abstracting energy from elastic fluid delivered thereto atsuper-acoustic velocity; said blades having convex and concave facesproviding blade passages and each convex face being polygonal to providethree or more corner portions; said corner portions being rounded andjoining successive fiat portions of the convex faces; said cornerportions of the convex faces defining, with respect to the concavefaces, throat sections and the fiat portions defining, with respect tothe concave faces, maximum sections ahead of, intermediate and followingthe throat sections of each passage and said throat and maximumsections,

being progressively larger in the di- 9. In a turbine, a row of bladeshaving concave and polygonal convex faces providing blade passages eachhaving a total turning angle ranging from 115 to 145, each polygonalface having three corner portions joining successive flat portions, thecorner portions of each passage being rounded and cooperating with theconcaveface thereof to provide throat sections which successivelyincrease in area in the direction of flow and the flat portions of eachpassage cooperating with the concave face to define maximum sectionssuccessively increasing in area in the direction of flow and from which,to the next throat section, thev passage converges and to which, fromthe preceding throat section, the passage diverges.

10. In a turbine, vane elements having convex and concavefaces'providing flow passages for elastic fluid moving at super-acousticvelocity, the convex faces of the fiow passages comprising fiat portionsjoined by rounded corner portions andproviding, with respect to theconcave faces, maximum and minimum sections, which, for each passage,are consecutively displaced angularly as determined by the area ratio ofthe sections and the exponent k of the isentropicpressure and specificvolume relationship of PV: constant and the turning angle to the initialthroat section of each passage being sufficiently smaller than thetheoretical as determined by the Mach number of the entering elasticfluid to avoid compression shocks at entrance.

11. In a turbine, vane elements having convex and concave faces definingfiow passages for elastic fiuid moving at super-acoustic velocity; theconvex face of each flow passage comprising a plurality of flatportions, including flat portions extending to the blade edges, andcorner portions for joining'successive fiat portions; said flat andcorner portions defining, respectively, with respect to the concaveface, maximum and minimum section areas such that fiuid in traversingthe passage undergoes compressions from each maximum section to thesucceeding minimum section and expansions from each of the latter to thesucceeding maximum section, the excess of actual velosity over theacoustic velocity at entrance and the successive compressions andexpansions being such that the velocity is reduced to the acoustic ateach minimum section and increased to super-acoustic values at maximumsections.

12. In a turbine, a row of impulse blades having concave and polygonalconvex faces defining passages for super-acoustic velocity elasticfluid, each of said convex faces having three rounded corners defining,with the concave face, minimum or throat sections for the passage andthe fiat portions of the polygonal face cooperating with the ends of theconcave face and with portions of the latter arranged lntermediately ofthe throat sections to provide maximum sections. said sections beingconsecutively displaced angularly as determined by the ratio of theareas of these sections and the exponent k" of the isentropic pressureand specific volume relationship PV =constant for the elastic fluidemployed, and the turning angle to the initial throat section beingsufiiciently smaller than the theoretical as determined by the Machnumber of the entering elastic fiuid to avoid compression shocks and thethroat section areas being made progressively larger in the direction offiow to accommodate for cooperating with having concave and polygonalconvex faces defining passages for super-acoustic velocity elasticfluid, each of said convex faces having a plurality of rounded cornersdefining, with the concave face, minimum or throat sections for the pas-I sage and the flat portions of the polygonal face the ends of theconcave race and with portions of the latter arranged intermediately ofthe throat sections to provide maximum sections, said sections beingconsecutively displaced angularly as determined by the ratio of theareas of these sections and the exponent k" of the isentropic pressureand specific volume relationship Pv =constant for the elastic fluidemployed and the throat section areas being made progressively larger inthe direction of flow to accommodate for friction.

' STEWART WAY.

